
Did the halo stars form in situ or were they accreted?
This is not yet clear, although it seems that at least a fraction of halo
stars have been accreted, since they show lower [\(\alpha \) /Fe] ratios. In fact,
the best tool
to ascertain this point is represented by the abundance ratios versus
metallicity relations. A recent
important discovery has been the realization that 10 Gyr ago a massive dwarf
galaxy, called Gaia-Enceladus or Gaia-Sausage, has fallen into the potential well of our
Galaxy. The stars of this object might represent a large fraction of the
stars accreted by the Galactic halo.

How should we explain the large spread observed in some abundance
ratios in halo stars?
The abundances and abundance ratios of neutron-process elements show a
particularly large spread observed in halo stars relative to other elements,
such as \(\alpha \) - and Fe-peak elements. The first explanation for
the spread is to assume inhomogeneous evolution of the halo, but then the
spread should be visible in all the elements. A tentative explanation was
given by [1]}, who suggested that the different extent of
the spread in the plot abundance ratio vs. metallicity is due to the
different nucleosynthesis and stellar progenitors of different elements,
coupled with inhomogeneous mixing.

How did the two disks form? Thick disk formed fast whereas the thin
formed slowly? Did the thin disk form inside-out?
The two Galactic disks could have formed in a sequential way but
with a halt in the star formation between the two, and by means of different
gas infall events (e.g., [2]}). Alternatively, the two disks could have formed in
parallel, out of two independent infall events but occurring at the same
time and at different rates (e.g., [3]}). In both
scenarios, the rate of chemical evolution must have been different in the two
disks, with the thick disk evolving faster than the thin disk.
Most of chemical models as well as chemo-dynamical cosmological simulations agree that
the thin disk should have formed on a longer
time scale than the thick disk and the halo. Late time major or minor mergers for the
formation of the thin disk seem to be excluded since they would have
cancelled the abundance gradients. On the other hand, abundance gradients
are favored by an inside-out formation of the thin disk, although other
processes such as inward gas flows and decreasing efficiency of star
formation with the Galactocentric distance should also be present
(e.g., [4]}, [5]}).

What is the cause of bimodality in the [\(\alpha \) /Fe] ratios in the
thick and thin disks, if real?
The cause of bimodality, if confirmed to be real, is certainly a consequence of the mechanisms and timescales for the formation of the two Galactic disks. The bimodality shows that thick disk stars have larger [\(\alpha \) /Fe] ratios than the thin disk stars and part of them lie in the same [Fe/H] range of thin disk stars, so that these abundance ratios appear in two sequences. The sequences look parallel in Gaia-ESO and AMBRE data, whereas in APOGEE data the low [\(\alpha \) /Fe] sequence appears rather as a plateau. This bimodal effect is indeed interesting, and it seems to be a common characteristic up to large Galactocentric distances ([6]}). In any case, many have been the explanations suggested for the bimodality. Several authors suggested that a framework like that of the two-infall model can explain the bimodality, since there is a stop in the star formation between the formation of the two disks with consequent dilution and decrease of the Fe abundance. This effect had been found first by [2]}, who showed that a gap in star formation of less than 1 Gyr was expected because of the second infall coupled with a threshold gas density for the
star formation. In order to explain APOGEE data, [8]} proposed a longer gap of \(\sim \)  4.3 Gyr, while [3]} proposed a parallel disk formation to explain the data of AMBRE survey. Other authors (e.g., [10]}, [11]}, [12]}, [13]}) have suggested that the bimodality is due to stellar migration. Also a late infall event occurring in the thin disk has been suggested (e.g., [14]}),
as well as the possibility that Gaia Enceladus can have influenced the evolution of the thick disk ([15]}).

How important is stellar migration?
Stellar migration seems indeed to exist and most of the studies suggest that it should occur mainly from the inner to the outer Galactic thin disk regions. However, there is not a general agreement on how really important is stellar migration. It has been invoked to solve several problems including the observed spread in the abundance patterns observed in the solar neighbourhood, the [\(\alpha \) /Fe] bimodality as well as the existence of the thick disk itself. On the other hand, models without stellar migration can still reproduce the majority of the observed features in the solar vicinity, except for the presence of stars with super solar metallicity, for which a 10–20% of migrated stars could be enough (see [16]}).
Anyway, the exact amount of solar vicinity stars which have migrated from other regions is still difficult to establish.

How did the bulge form? How many different stellar populations are in the bulge?
Most of the chemical studies, including chemo-dynamical cosmological simulations, relative to the Galactic bulge have suggested that
it formed quickly, as a consequence of a strong burst of star formation lasting less than 1 Gyr. With high star formation efficiency, short infall timescale and an IMF with more massive stars than in the solar neighbourhood, it is possible to reproduce the MDF and the [X/Fe] vs. [Fe/H] relations for a large part of bulge stars, as first shown by [17]}. However, there is a fraction of bulge stars which are more metal rich and associated to the Boxy/Peanut X-shaped bulge ([18]}), and might have been accreted from the inner disk. The true bulge stars seem to be old and the fraction of stars younger than 5 Gyr to be no more than 10% (e.g., [19]}, although other studies have suggested a larger fraction of young stars, such as [20]}).

How did abundance gradients along the thin disk formed? Which is the role of radial gas flows?
Abundance gradients are present along the thin disk: they have been derived from young stars, PNe and HII regions. The abundance gradients generally indicate the present time abundances along the disk, except perhaps for data of PNe which can refer also to older objects. Chemical evolution models predict abundance gradients if there is a gradient in the SFR along the disk. This can be obtained in several ways: i) by assuming an inside-out formation of the disk by means of gas infall, with the infall timescale increasing with Galactocentric distance (e.g., [21]}, [22]}, ii) with an efficiency of star formation decreasing with Galactocentric distance (e.g., [23]}, [24]}), iii) by assuming a gas threshold for star formation ([22]}), iv) by varying the IMF with Galactocentric distance, although this variation should imply a smaller number of massive stars at larger Galactocentric distances, at variance with the [26]} criterion for star formation; v) by assuming radial gas flows (e.g., [27]}, [28]}, [29]}, [5]}). All of these processes can be at work at the same time but while we could avoid ii), iii) and iv), we cannot exclude i) and v).
In fact, radial gas flows and inside-out formation seem to be unavoidable physical processes: in particular, the inward radial gas flows have a strong effect on the formation of abundance gradients and they are the natural consequence of gas infall. The inside-out process derives from a faster accretion in the inner denser disk regions relative to the less dense outer ones (see [31]}).
In addition, most of the chemo-dynamical cosmological simulation found that the disk of a Milky Way-like spiral forms inside-out.
Another still open question is whether the abundance gradients have steepened or flattened in time, depending mostly on the assumptions on the SFR. For example, by assuming a constant star formation efficiency leads to a steepening of the gradients in time while a variable efficiency as a function of Galactic radius induces a flattening of gradients with time. This problem will be solved only when we will have more data on gradients shown by old stars.

Which stars are the main contributors of r-process elements? Merging
neutron stars or supernovae or both?
The r-process elements, such as Eu, are mainly formed in massive stars either by means of explosive nucleosynthesis during the CC-SN events and/or by merging neutron stars. The second channel seems to be favored, as shown by the heavy elements which arose from the merging neutron star event associated to the detection of GW170817 ([32]}). Chemical evolution studies have explored the possibility that Eu can be produced only by merging events of compact objects (neutron stars and black holes) as well as by CC-SNe or both. In fact, CC-SNe alone seem to be not able to produce the right quantity of Eu to reproduce its solar abundance. The plot of [Eu/Fe] vs. [Fe/H] clearly shows that Eu behaves like an \(\alpha \) -element, namely it shows a plateau of [Eu/Fe] at low metallicity followed by a decrease of this ratio at higher metallicities. This behaviour is interpreted by means of the time-delay model, in which elements formed on short timescales (by massive stars), such as \(\alpha \) -elements, at low metallicity show an overabundance relative to Fe, which is mainly formed and ejected by Type Ia SNe on longer timescales.
Therefore, from a chemical point of view, the mergers of compact objects can be the main source of Eu, if the merging timescale is very short. [33]} suggested that all systems should merge in a time of 1 Myr, otherwise one should assume a distribution of merging times together with CC-SNe also contributing to Eu. This conclusion was shared by papers in the following years (e.g., [34]}, [35]}, [36]}, [37]}), unless one assumes that the fraction of merging systems should have been higher at early times (e.g., [38]}, [39]}).

Why the origin of some elements is not yet understood? 
When we compare the predicted [X/Fe] vs. [Fe/H] relations with observations in the solar vicinity and bulge, we find that for some elements there is no agreement and these elements mainly belong to the Fe-peak group. Some of them do not behave like Fe, as one would expect on the basis of the time-delay model, and this fact suggests that we have not yet understood the nucleosynthesis of such elements, which are \(^{51}\) V, \(^{52}\) Cr, \(^{55}\) Mn, \(^{59}\) Co and \(^{64}\) Zn. Other elements, which do not belong to the Fe-peak element group, and whose nucleosynthesis is not yet well understood are \(^{41}\) K and \(^{48}\) Ti. Generally, in chemical evolution models, the yields of the above mentioned species need to be changed (increased or decreased) relative to standard nucleosynthesis calculations, in order to reproduce their abundance patterns (e.g., [40]}, [41]}). Future improvements in stellar and nucleosynthesis models are expected to shed light on the origin of these elements.

